A079407 Numbers m such that the least s >= 0 such that Sum_{k=0..m} (k+s)!/C(m,k) is an integer satisfies s = m - 1.

1, 2, 4, 5, 13, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset

1,2

Comments

The prime numbers that are not in this sequence are 3, 7, 11, 29, 157, 211, 233, 419, ... - Jinyuan Wang, Apr 03 2020

Links

Table of n, a(n) for n=1..58.

Prog

(PARI) for(n=1, 150, s=0; while(frac(sum(k=0, n, (k+s)!/binomial(n, k)))>0, s++); if(n-s==1, print1(n, ", ")))

Crossrefs

Sequence in context: A102932 A128457 A139485 * A078652 A289491 A102992

Adjacent sequences: A079404 A079405 A079406 * A079408 A079409 A079410

Keyword

nonn

Author

Benoit Cloitre, Feb 16 2003

Extensions

More terms from Jinyuan Wang, Apr 03 2020

Status

approved